Franklin

Which Numbers are Real?.

Author/Creator:
Henle, Michael.
Publication:
Washington : American Mathematical Society, 2012.
Format/Description:
Book
1 online resource (230 pages)
Series:
Classroom Resource Materials
Classroom Resource Materials
Status/Location:
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Other records:
Subjects:
Numbers, Real.
Numbers, Complex.
Number theory.
Form/Genre:
Electronic books.
Contents:
cover
copyright page
title page
Introduction
Contents
I THE REALS
Axioms for the Reals
How to Build a Number System
The Field Axioms
The Order Axioms
The Completeness Axiom
Construction of the Reals
Cantor's Construction
Dedekind's Construction of the Reals
Uniqueness of the Reals
The Differential Calculus
A Final Word about the Reals
II MULTI- DIMENSIONAL NUMBERS
The Complex Numbers
Two-Dimensional Algebra and Geometry
The Polar Form of a Complex Number
Uniqueness of the Complex Numbers
Complex Calculus
A Final Word about the Complexes
The Quaternions
Four-Dimensional Algebra and Geometry
The Polar Form of a Quaternion
Complex Quaternions and the Quaternion Calculus
A Final Word about the Quaternions
III ALTERNATIVE LINES
The Constructive Reals
Constructivist Criticism of Classical Mathematics
The Constructivization of Mathematics
The Definition of the Constructive Reals
The Geometry of the Constructive Reals
Completeness of the Constructive Reals
The Constructive Calculus
A Final Word about the Constructive Reals
The Hyperreals
Formal Languages
A Language for the Hyperreals
Construction of the Hyperreals
The Transfer Principle
The Nature of the Hyperreal Line
The Hyperreal Calculus
Construction of an Ultrafilter
A Final Word about the Hyperreals
The Surreals
Combinatorial Games
The Preferential Ordering of Games
The Arithmetic of Games
The Surreal Numbers
The Nature of the Surreal Line
More Surreal Numbers
Analyzing Games with Numbers
A Final Word about the Surreals
Bibliography
Index
About the Author.
Notes:
Description based on publisher supplied metadata and other sources.
Local notes:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Other format:
Print version: Henle, Michael Which Numbers are Real?
ISBN:
9781614441076
9780883857779
OCLC:
817966939